Interpretation:
The density of a billiard ball and a collection of billiards ball packed in simple unit cell and aface-centered unit cell are to be determined, and the reason that they are different is to be explained.
Concept Introduction:
A crystal lattice is made of small repeating unit cells.
A unit cell is of a primitive or a centered type. The spheres in a unit cell represent an atom, molecule, or ion.
Each sphere is shared by adjacent cells. The spheres at the corners are shared by eight unit cells. A sphere in the centre of each face is shared by two unit cells.
Volume of a sphere is
Here,
Volume of a unit cell
Here,
Density of unit cell is mass divided by volume.
Here,
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